Question

1. In general, the sample mean is a better estimator of the population mean for larger sample sizes.

		True
		False

2.

If events  A and  B are not mutually exclusive, then it is possible that  P( A) +  P( B) > 1.

		True
		False

3.

What method of data collection would you use to collect data for a study where a drug was given to 95 patients and a placebo to another group of 95 patients to determine if the drug has an effect on a patient's illness?

		designed experiment
		observational study
		published source
		survey

Answer 1

1.True

The sample mean of a group of observations is an estimate of population mean.

The central limit theorem says "for a large enough sample size n., the distribution of sample size approaches a normal distribution".

Although varience is much smaller, the sample mean of distribution is identical to the mean of population distribution.

So the statement is true.

2.True

Two events are said tobe not mutually exclusive if there is atleast one common outcome between the events A and B.

Let S be the sample space for rolling a die.

S={1,2,3,4,5,6}

Let P(A) be the probability of getting an even number.

Here we have 2,4 or 6 as even numbers.

Let P(B) be the probability of getting a number less than 5.

Here we have 1,2,3,4 as less than 5.

So A and B are said to be mutually non exclusive as they have 2 and 4 as common.

Probability= Number of favouable outcomes/Number of posible outcomes

P(A)= 3/6=1/2

P(B)=4/6=2/3

P(A)+P(B)=1/2+2/3=1.16 (greater than 1)

So the statement is true

3.Observational study

In observational study, the researchers collect data only by observing the subjects and do not influence the outcome.

Here , in our question,while gving drug to 95 patients and placebo to another group of 95 patients, observational study is the best metod for data colection.

In Designed experiment method, the researcheers run a set of task and keeps on varying the input to study the variations in the output.

Published sources are statistical synopses and other reports done by differnt departments of government.

Asurvey is an investigation about a give population often done by collecting data from a sample of population.

So the correct answer is observational study.